Doped cylinders: The nature of the lightly doped system clearly depends on the character of the undoped parent state. The resulting phase diagram has not been nearly as thoroughly investigated as in the case of the square lattice. Particularly interesting is the fate of a lightly doped spin liquid. A spin liquid can be thought of as a quantum disordered superconductor, such that upon light doping, the “pairing” is a property inherited from the insulating state while the superfluid stiffness (and hence the ordering temperature) vanishes continuously as \(x \rightarrow 0\)  [1]}, [2]}, [3]}. Specifically, light doping of a gapped \({\mathbb {Z}}^{\vphantom{\dagger }}_2\)  spin liquid could lead to a gapped superconductor - with the “superconducting” gap derived from the spin-liquid gap - which is chiral (\(d+id\) ) [4]} or non-chiral depending on the nature of the spin-liquid from which it arose - while a nodal spin liquid naturally connects to a nodal superconductor [5]}.
There is preliminary DMRG evidence that each of these may occur on the triangular lattice under appropriate circumstances [6]}, [7]}, [8]}, [9]}.
